Gravitational fields as generalized string models

TL;DR

This paper demonstrates that Einstein's equations for stationary axisymmetric vacuum fields can be reformulated as equations for bosonic strings on a nonflat background, providing a new geometric perspective on gravitational fields with symmetries.

Contribution

It introduces a novel string-theoretic representation of certain gravitational fields using generalized harmonic maps and the concept of dimensional extension.

Findings

Einstein's equations are equivalent to string motion equations in this framework.

The approach applies to any gravitational field with two commuting Killing vectors.

A new geometric interpretation of stationary axisymmetric vacuum solutions is provided.

Abstract

We show that Einstein's main equations for stationary axisymmetric fields in vacuum are equivalent to the motion equations for bosonic strings moving on a special nonflat background. This new representation is based on the analysis of generalized harmonic maps in which the metric of the target space explicitly depends on the parametrization of the base space. It is shown that this representation is valid for any gravitational field which possesses two commuting Killing vector fields. We introduce the concept of dimensional extension which allows us to consider this type of gravitational fields as strings embedded in D-dimensional nonflat backgrounds, even in the limiting case where the Killing vector fields are hypersurface orthogonal.